Liang et al. [1]} define a complexity measure using the Fisher-Rao norm to investigate model generalization capability.
They suggest that a complexity measure used to study generalization should satisfy the invariance property. The invariance property requires that the generalization capacity depends on the equivalence classes obtained by deep models. In other words, many different parameterizations may lead to the same prediction. Thus, the specific parameterization of deep models should not affect the generalization and the complexity measure.
They show that the Fisher-Rao norm honors this invariance property and thus is able to explain the generalization capability of deep learning models.
